Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
172 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #99 |
| commutator | C22×C4 | C42 |
| Frattini, cosocle | C2×#117 | C22 |
| socle | C22 | #342 |
| prime radical | C24 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ G | |
| LECS | G ▷ C2×#117 ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4⋊C8 | C4 | semidirect |
| 8. C2×C4⋊C8 | C4 | semidirect |
| 13. #324 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1798 | 2 |
| #1740 | 2 |
| #1458 | 2 |